Newton Numbers and Residual Measures of Plurisubharmonic Functions

1999/05/11 by Alexander Rashkovskii, Rashkovskii, Alexander
Mathematics · #32F05 #32F07 #Complex Variables (math.CV) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #Holomorphic and Operator Theory #math.CV #msc:32F05 #msc:32F07

paper · pdf · doi:10.48550/arxiv.math/9905062

21 pages, LaTeX

arxiv created 1999/05/11 · openalex publication_date 1999/05/11 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We study the masses charged by (dd^cu)ⁿ at isolated singularity points of plurisubharmonic functions u. It is done by means of the local indicators of plurisubharmonic functions. As a consequence, bounds for the masses are obtained in terms of the directional Lelong numbers of u, and the notion of the Newton number for a holomorphic mapping is extended to arbitrary plurisubharmonic functions. We also describe the local indicator of u as the logarithmic tangent to u.

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